Zinc oxide is a material having electrically semiconductive, photoconductive and piezoelectric properties. There has been known a method for producing through a spattering or CVD process a zinc oxide material having suitable transparency and crystal-axis orientation for use as materials of piezoelectric or optoelectronics components (Japanese Patent Laid-Open Publication No. Hei 05-254991). A method has also been known for producing a transparent zinc oxide material having an electrically conductive or insulative property by doping zinc oxide of material with a doping material (Japanese Patent Laid-Open Publication No. Hei 05-070286). Further, a hydrothermal process has been known as a method for producing a piezoelectric semiconductor composed of a single crystal including zinc oxide as a primary component (Japanese Patent Laid-Open Publications No. Hei 06-279192, 06-279193, etc.). However, for such zinc oxide materials, it has not been reported to achieve a ferromagnetic state therein successfully.